In this paper we study nonlinear programming problems with equality, inequality, and abstract constraints where some of the functions are Fréchet differentiable at the optimal solution, some of the functions are Lipschitz near the optimal solution, and the abstract constraint set may be nonconvex. We derive Fritz John type and Karush–Kuhn–Tucker (KKT) type first order necessary optimality condi...

We consider optimization problems with equality, inequality, and abstract set constraints, and we explore various characteristics of the constraint set that imply the existence of Lagrange multipliers. We prove a generalized version of the Fritz-John theorem, and we introduce new and general conditions that extend and unify the major constraint qualifications. Among these conditions, two new pr...

We consider optimization problems with equality, inequality, and abstract set constraints, and we explore various characteristics of the constraint set that imply the existence of Lagrange multipliers. We prove a generalized version of the Fritz-John theorem, and we introduce new and general conditions that extend and unify the major constraint qualifications. Among these conditions, two new pr...

We consider optimization problems with equality, inequality, and abstract set constraints, and we explore various characteristics of the constraint set that imply the existence of Lagrange multipliers. We prove a generalized version of the Fritz–John theorem, and we introduce new and general conditions that extend and unify the major constraint qualifications. Among these conditions, two new pr...

(ABSTRACT) The containership design problem involves optimizing a nonconvex objective function over a design space that is restricted by a set of constraints defined in terms of nonconvex functions. An application of standard nonlinear optimization methods to such a problem can at best attain a local optimum that need not be a global optimum. This thesis investigates the application of alternat...

Nowadays, many researchers are working on Constraint Satisfaction Problems (CSPs). Many CSPs can be modelled as non-binary CSPs and, theoretically, they can be transformed into an equivalent binary CSP, using some of the current techniques. However, this transformation may be an inadequate or inefficient way to manage certain types of non-binary constraints. In this paper, we propose an algorit...

The Algebraic Dichotomy Conjecture states that the Constraint Satisfaction Problem over a fixed template is solvable in polynomial time if the algebra of polymorphisms associated to the template lies in a Taylor variety, and is NP-complete otherwise. This paper provides two new characterizations of finitely generated Taylor varieties. The first characterization is using absorbing subalgebras an...

Arc-consistency algorithms are widely used to prune the search space of Constraint Satisfaction Problems (CSPs). One of the most well-known arc-consistency algorithms for filtering CSPs is AC3. This algorithm repeatedly carries out revisions and requires support checks for identifying and deleting all unsupported values from the domains. Nevertheless, many revisions are ineffective, that is, th...

Bang-Jensen and Hell conjectured in 1990 (using the language of graph homomorphisms) a CSP dichotomy for digraphs with no sources or sinks. The conjecture states that the constraint satisfaction problem for such a digraph is tractable if each component of its core is a circle and is NP-complete otherwise. In this paper we prove this conjecture, and, as a consequence, a conjecture of Bang-Jensen...